JACOBI PSEUDOSPECTRAL METHOD FOR FOURTH ORDER PROBLEMS  

作　　者：Zheng-su Wan Ben-yu Guo Zhong-qing Wang 

机构地区：[1]Department of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China [2]Department of Mathematics, Shanghai Normal University, 200234, China [3]Division of Computational Science of Einstitute of Shanghai Universities

出　　处：《Journal of Computational Mathematics》2006年第4期481-500,共20页计算数学（英文）

基　　金：The work of these authors is supported in part by NSF of China, N.10471095, Science Foundation of Shanghai N.04JC14062, Special Funds for Doctorial Authorities of Chinese Education Ministry N.20040270002, Shanghai Leading Academic Discipline Project N.T0401, E-institutes of Shanghai Municipal Education Commission, N.E03004, Special Funds for Major Specialities and Fund N.04DB15 of Shanghai Education Commission.

摘　　要：In this paper, we investigate Jacobi pseudospectral method for fourth order problems. We establish some basic results on the Jacobi-Gauss-type interpolations in non-uniformly weighted Sobolev spaces, which serve as important tools in analysis of numerical quadratures, and numerical methods of differential and integral equations. Then we propose Jacobi pseudospectral schemes for several singular problems and multiple-dimensional problems of fourth order. Numerical results demonstrate the spectral accuracy of these schemes, and coincide well with theoretical analysis.In this paper, we investigate Jacobi pseudospectral method for fourth order problems. We establish some basic results on the Jacobi-Gauss-type interpolations in non-uniformly weighted Sobolev spaces, which serve as important tools in analysis of numerical quadratures, and numerical methods of differential and integral equations. Then we propose Jacobi pseudospectral schemes for several singular problems and multiple-dimensional problems of fourth order. Numerical results demonstrate the spectral accuracy of these schemes, and coincide well with theoretical analysis.

关 键 词：Jacobi pseudospectral method Differential equations of fourth order Singular problems. 

分 类 号：O175[理学—数学]